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To lay tile on the diagonal, put a speed square in the corner you are starting from and snap a chalk line.
Cut a few tiles on the wet saw and lay them out on the floor for a dryfit. You should mix tiles from different boxes to account for the color variations.
Backbutter the tiles with thinset using a square-notch trowel. The slate tile thickness can vary up to 7/16" of an inch so add extra thinset if necessary to make up the difference. Hold the trowel almost vertically to get the maximum coverage of thinset.